Prony proposed 1795 a method to solve the parameter reconstruction problem for exponential
sums in the univariate case. The key idea is to consider an associated polynomial equation
and to study an equivalent algebraic problem.

In this talk, we present a generalization of Prony?s method to the multivariate case.
We discuss related algebraic problems and methods. The talk is based on joint work with Stefan
Kunis, Thomas Peter and Ulrich von der Ohe.
...

In this lecture, I will give some basic properties of the Castelnuovo-Mumford regularity and its
applications to bound Hilbert coecients.

1. Denition and some basic properties

In this part, I will give the denition of the Castelnuovo-Mumford regularity by using local cohomology.
Then I will recall basic properties such as Castelnuovo's lemma and the relation of the Castelnuovo-Mumford
regularities of modules in an exact sequence.